A consortium made up of Spanish lender Bankinter and U.S. investment fund Apollo Global Management isseen as the frontrunner to buy BSI, although it offered"substantially less" than the insurer's estimate in 2012 of itsworth, two of the people with direct knowledge of the mattersaid.

That places Generali, which had set an April 30 finaldeadline for bids, in a tough situation as it needs to raisemoney but doesn't want to sell assets too cheaply.

Italy's Generali, which built up BSI through a series ofacquisitions before the financial crisis hit, has been trying tosell BSI for more than two years, all the sources said. It isnow left with two options: selling BSI for less than it thinksis its underlying value, or calling the sale off.

It is also selling its life reinsurance business in the U.S.in a deal worth between $800 million and $1 billion.

Generali, Bankinter and Apollo declined to comment.

Swiss private bank Safra and Chinese investment fund HonyCapital had earlier expressed an interest for BSI. It is howevernot clear if they are still interested, the sources said.

Safra declined to comment while Hony Capital was notimmediately available for comment.

Generali could decide to call off the sale and explore otheroptions such as a public listing of BSI, one of the sourcessaid.

"This would buy them time in the hope BSI will post betterresults in the next quarter", the source said.

Bankinter is one of Spain's healthier banks, with lessexposure than others to a damaging property boom and bust, whichultimately led Spain to ask Europe for a 40 billion euro bankbailout.

Bankinter still had to team up with a financial player to beable to bid for BSI, two of the people said. The bank announcedon Monday it would seek to raise an additional 94 million eurosin capital to meet new European solvency ratios.

Bankinter was also interested in acquiring Belgian bankKBC's private bank KBL but lost it to Qatari-backed Luxembourgfirm Precision Capital in 2011, one of the people said.

Japanese firms Mizuho Bank, Sumitomo Corp and players in Qatar and Abu Dhabi have also showninterest in BSI, but had not made offers by the deadline, allthe sources said.